Solve for $p$, $ \dfrac{3p - 10}{10p} = \dfrac{6}{25p} - \dfrac{3}{5p} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10p$ $25p$ and $5p$ The common denominator is $50p$ To get $50p$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{3p - 10}{10p} \times \dfrac{5}{5} = \dfrac{15p - 50}{50p} $ To get $50p$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{6}{25p} \times \dfrac{2}{2} = \dfrac{12}{50p} $ To get $50p$ in the denominator of the third term, multiply it by $\frac{10}{10}$ $ -\dfrac{3}{5p} \times \dfrac{10}{10} = -\dfrac{30}{50p} $ This give us: $ \dfrac{15p - 50}{50p} = \dfrac{12}{50p} - \dfrac{30}{50p} $ If we multiply both sides of the equation by $50p$ , we get: $ 15p - 50 = 12 - 30$ $ 15p - 50 = -18$ $ 15p = 32 $ $ p = \dfrac{32}{15}$